Quasi One-Dimensional Bosons in Three-dimensional Traps: From Strong Coupling to Weak Coupling Regime

Abstract

We analyze a recent experiment on a Tonks-Girardeau gas of ${}^{87}$Rb atoms (T. Kinoshita, T. Wenger, and D.S. Weiss, Science {\bf 305}, 1125 (2004)). We find that the experimental data are compatible with the one-dimensional theory of Lieb, Seiringer and Yngvason (Phys. Rev. Lett. {\bf 91}, 150401 (2003)) but are better described by a theory that takes into account variations in the transverse width of the atomic cloud. By using this theory we investigate also the free axial expansion of the ${}^{87}$Rb gas in different regimes: Tonks-Girardeau gas, one-dimensional Bose-Einstein condensate and three-dimensional Bose-Einstein condensate.

4 pages, 4 figures, accepted for publication in Phys. Rev. A

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